I realize some items are configured such as Deleted Items Purge. But what actually triggers these events to start and when do they run. Are there maintenance theads running constantly? How long shoud it take when I accept a meeting until the organizer sees my status change? Are there any logs that show these types of activies (other than scheduling)?

For events are there priorities or is it first-in first-out regardless of whether its a new meeting, meeting change or a old meeting delete; big or small attendee list; recurring/not recurring?

Any information on the inner workings that would allow us to better understand what is going on would be greatly appreciated.

Right now we don't have a dedicated maintenance thread. The tasks are handled by the normal server threads. We use DB queues to schedule and execute operations like scheduling and notifications. Timestamps are set on entries to trigger purge/expiration of the entry at the right time.
Scheduling right now is done on a purely first come, first handled basis. For most part, the scheduling changes should be reflected in all parties' copies almost immediately.
For more information on Notification, see https://wikis.oracle.com/display/CommSuite/Using+Calendar+Server+7+Notifications .